Question: Jessica is 2 times as old as Stephanie. 30 years ago, Jessica was 8 times as old as Stephanie. How old is Jessica now?
Answer: We can use the given information to write down two equations that describe the ages of Jessica and Stephanie. Let Jessica's current age be $j$ and Stephanie's current age be $s$ The information in the first sentence can be expressed in the following equation: $j = 2s$ 30 years ago, Jessica was $j - 30$ years old, and Stephanie was $s - 30$ years old. The information in the second sentence can be expressed in the following equation: $j - 30 = 8(s - 30)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to solve our first equation for $s$ and substitute it into our second equation. Solving our first equation for $s$ , we get: $s = j / 2$ . Substituting this into our second equation, we get: $j - 30 = 8($ $(j / 2)$ $- 30)$ which combines the information about $j$ from both of our original equations. Simplifying the right side of this equation, we get: $j - 30 = 4 j - 240$ Solving for $j$ , we get: $3 j = 210$ $j = \dfrac{1}{3} \cdot 210 = 70$.